Abstract: We study mobile systems, i.e. systems
with a dynamically changing communication topology, from a process
algebras point of view. Mobility can be introduced in process
algebras by allowing names or terms to be transmitted. We
distinguish these two approaches as first-order and
higher-order. The major target of the thesis is the
comparison between them.

The prototypical calculus in the first-order paradigm is the
pi-calculus. By generalising its sort discipline we derive
an w-order extension called Higher-Order
pi-calculus (HO-pi). We show that such an extension does not
add expressiveness to the pi-calculus: Higher-order processes can
be faithfully compiled down to first-order, and respecting the
behavioural equivalence we adopted in the calculi. Such an
equivalence is based on the notion of bisimulation, a fundamental
concept of process algebras. Unfortunately, the standard definition
of bisimulation is unsatisfactory in a higher-order calculus
because it is over-discriminating. To overcome the problem, we
propose barbed bisimulation. Its advantage is that it can
be defined uniformly in different calculi because it only
requires that the calculus possesses an interaction or
reduction relation. As a test for barbed bisimulation, we
show that in CCS and pi-calculus, it allows us to recover the
familiar bisimulation-based equivalences. We also give simpler
characterisations of the equivalences utilised in HO-pi. For this
we exploit a special kind of agents called triggers, with
which it is possible to reason fairly efficiently in a higher-order
calculus notwithstanding the complexity of its transitions.

Finally, we use the compilation from HO-pi to pi-calculus to
investigate Milner's encodings of lambda-calculus into pi-calculus.
We present analogous encodings of lambda-calculus into HO-pi. By
comparison with those into pi-calculus, these are easier to
understand and with a closer correspondence between reduction on
lambda-terms and on their process counterparts. We show that the
two encodings of lazy lambda-calculus and the compilation from
HO-pi to pi-calculus commute. Thus we can reason in HO-pi and the
results hold for pi-calculus as well. In this way we are able to
derive a direct characterisation of the equivalence upon
lambda-terms induced by Milner's encoding and by the behavioural
equivalence adopted on the process terms.

From the representability result of HO-pi in pi-calculus we
conclude that the first-order paradigm, which enjoys a simpler and
more intuitive theory, should be taken as basic.
Nevertheless, the study of the lambda-calculus encodings shows that
a higher-order calculus can be very useful for reasoning at a more
abstract level.